I don't think that is the case here. I mean in general and historically speaking, yes that's the fate of brother princes but I remember during the war (towards the end), the crown prince said something to his brother like "do you have to fight for the throne?" or something like that and Mil replied that he has to do it...I don't think the crown prince was just asking him to die, I think he was asking him to stop fighting for the throne, in which case Mil doesn't die. But probably his mom and his supporters will suffer and rightfully so.
As for Mil saying the crown prince will kill him, I think he meant if they fight and he (Mil) loses and not, in general, he'll kill him even if he doesn't fight. So Mil means if they go at it and he loses he'll die which makes sense.
I know Mil is too invested in this and has many people backing him up and he'll suffer even if he doesn't fight for the throne because his supporters will feel betrayed. But I just can't understand killing your brother and making your father watch you do so just to save a couple of criminal family members. I know you said he isn't close to his brother but he isn't close to his uncle either...his mom has been crazy for years so he can't be that close to her either ...so basically, he isn't close to anyone so his actions shouldn't be justified by close family relationships. If he's fighting for blood ties then he is tied the same way to his brother and father.
Before this chapter, I thought something has happened in which both parties were equally guilty so I never completely supported one prince over the other especially because Mil was her ally in her previous life were no one else cared for her but after this chapter, I can't do the same. Mil's side of the family was 100% in the wrong and I can't support him even 1% knowing he wants criminals to escape justice

I like Mil and all but his family needs to suffer for what they did and I respect him a lot less knowing that he is supporting his mom and uncle knowing they produced false evidence and knowing all their wrongdoings... His brother and father are family too and he knows that he'll kill his brother and torture his brother to get the throne and save his mom and uncle and that makes no sense because he is saving bastards and killing good family members... It's not like he is saving family at the expense of strangers...
I used to somewhat pity his mother seeing her current state but now, I just hope we see more of her suffering. She fully deserves it